Question: Simplify the following expression: $ n = \dfrac{1}{7} - \dfrac{k - 1}{-4k} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-4k}{-4k}$ $ \dfrac{1}{7} \times \dfrac{-4k}{-4k} = \dfrac{-4k}{-28k} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{k - 1}{-4k} \times \dfrac{7}{7} = \dfrac{7k - 7}{-28k} $ Therefore $ n = \dfrac{-4k}{-28k} - \dfrac{7k - 7}{-28k} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{-4k - (7k - 7) }{-28k} $ Distribute the negative sign: $n = \dfrac{-4k - 7k + 7}{-28k}$ $n = \dfrac{-11k + 7}{-28k}$ Simplify the expression by dividing the numerator and denominator by -1: $n = \dfrac{11k - 7}{28k}$